Repairing a Mirror Modifier centre-line non-manifold edges (2.8)
Select all vertices in your mesh and hit Alt-M.  From the drop-down, choose "By Distance".  You can also change the "distance" at the bottom-left corner of the window.  Here's a picture to show you where.



It looks to me like this is pretty much the same as the "Remove Doubles" option.  Hope this helps!

P.S.  If you have two vertices that are not at the same position, and you want them to merge to the position of a certain one of those vertices, you select the vertex that has the desired position first, then select the other and merge them, using the drop-down option "At First".  Hope that makes sense.